Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Hydrostatic pressure and its measurement
Question Statement:
Which of the following statements regarding the center of pressure ($h_{cp}$) on a submerged vertical plane surface of area $A$ immersed in a homogeneous static liquid are correct?
Options:
(A) The center of pressure always lies strictly below the centroid of the immersed surface area
(B) The distance between the centroid and center of pressure is given by $\frac{I_G}{\bar{h} A}$, where $I_G$ is second moment of area about the horizontal centroidal axis
(C) As the immersion depth $\bar{h}$ increases indefinitely, the center of pressure asymptotically approaches the centroid of the area
(D) The vertical depth of the center of pressure depends directly on the dynamic viscosity of the liquid
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
- Statements A, B, and C are correct:
1. $h_{cp} = \bar{h} + \frac{I_G}{\bar{h} A}$. Since $I_G > 0$ and $\bar{h} A > 0$, $h_{cp} > \bar{h}$, placing the center of pressure below the centroid.
2. The eccentric offset is $\frac{I_G}{\bar{h} A}$.
3. As $\bar{h} \to \infty$, $\frac{I_G}{\bar{h} A} \to 0$, so $h_{cp} \to \bar{h}$.
- Statement D is incorrect: Hydrostatic pressure distribution depends only on fluid specific weight $\gamma = \rho g$ and depth $h$; dynamic viscosity $\mu$ has zero effect in static equilibrium.